Which is a correct first step for solving this equation? - 32 + 2 - 52

Parabola Equations - Algebra

mash [69]

Answer:

$h=-\frac{1}{6}x^2+2x$

Step-by-step explanation:

The height of the tunnel is modeled by:

$h=rx^2+tx$

Where r and t are constants.

We know that the maximum height of the tunnel h is 6 meters.

And at ground level, the width is 12 meters.

And we want to determine the equation of the parabola.

First, since this is a quadratic, our maximum height h will occur at the vertex of our equation.

The vertex is given by:

$(-\frac{b}{2a}, f(-\frac{b}{2a}))$

In our case, we have the function:

$h=(r)x^2+(t)x$

Hence, a=r; b=t; and c=0.

Therefore, our vertex is:

$\Rightarrow -\frac{t}{2r}$

Thus, if we substitute this back into our equation, we should get 6 since 6 is the maximum height which is determine by the vertex. In other words:

$(6)=r(-\frac{t}{2r})^2+t(-\frac{t}{2r})$

Simplify:

$6=r(\frac{t^2}{4r^2})-\frac{t^2}{2r}$

Simplify:

$6=\frac{t^2}{4r}-\frac{t^2}{2r}$

Combine fractions:

$6=\frac{t^2}{4r}-\frac{2t^2}{4r}=\frac{-t^2}{4r}$

Multiply both sides by the denominator:

$24r=-t^2$

Let's solve for the constant r. Divide both sides by 24. Hence:

$r=-\frac{t^2}{24}$

Now, we can use our knowledge of the width.

We know that the width is 12 meters at ground level.

Hence, when h=0, the difference of our roots is 12.

So:

$0=rx^2+tx$

We can factor:

$0=x(rx+t)$

By the Zero Product Property:

$x=0\text{ or } rx+t=0$

So, the first zero is 0.

Therefore, the second zero must be 12 to ensure that our width is 12.

Let's isolate the second zero. Subtract t from both sides:

$rx=-t$

Divide both sides by r:

$x=-\frac{t}{r}$

We know that this zero must be 12. Thus:

$12=-\frac{t}{r}$

We have previously solved for r. Substitute:

$12=-\frac{t}{\frac{-t^2}{24}}$

Simplify:

$12=\frac{24}{t}$

Take the reciprocal of both sides:

$\frac{t}{24}=\frac{1}{12}$

Multiply both sides by 24. Hence, the value of t is:

$t=2$

Now, we can find r. r is given by:

$r=-\frac{t^2}{24}$

By substituting 2 for t, then, we acquire that:

$r=-\frac{(2)^2}{24}=-\frac{4}{24}=-\frac{1}{6}$

Therefore, for:

$h=rx^2+tx$

Our equation is:

$h=-\frac{1}{6}x^2+2x$

7 0

3 years ago

According to historical records, the Great Pyramid of Giza was originally about 147 meters tall. Assuming it was built with its

vivado [14]

Answer:

115m

Step-by-step explanation:

Note that one of the face of a pyramid is a right angled triangle.

Since the pyramid was about 147m tall, the height of triangle will be 147m. If one of the faces is built with one of its faces at 52° to the incline, we can find the original length of one of its sides using SOH CAH TOA

tan(theta) = opposite/adjacent

Given theta = 52°, opposite = 147m (the side directly opposite the angle)

Substituting we have;

Tan52° = 147/adjacent

Adjacent = 147/tan52°

Adjacent = 114.8m

= 115m

Therefore 115m is the original length of one of its side

6 0

4 years ago

A gardener makes a new circular flower bed. The bed is teen feet in diameter. Calculate the circumference and the area of the ci

KATRIN_1 [288]

Answer:

I. Circumference of circular flower bed = 31.42 ft.

II. Area of circular flower bed = 78.55 ft²

Step-by-step explanation:

Given the following data;

Diameter = 10 ft

Radius = diameter/2

Radius = 10/2

Radius, r = 5 ft

I. To find the circumference of the circular flower bed;

Circumference of circle = 2πr

Substituting into the formula, we have

Circumference of circular flower bed = 2*3.142*5

Circumference of circular flower bed = 31.42 ft

II. To find the area;

Area of circle = πr²

Substituting into the formula, we have;

Area of circular flower bed = 3.142*5²

Area of circular flower bed = 3.142*25

Area of circular flower bed = 78.55 ft²

8 0

3 years ago

Which elements make up the stars

leonid [27]

Answer:

Most stars have small amounts of heavy elements like carbon, nitrogen, oxygen and iron. But the shine from the stars comes from burning hydrogen into helium in their cores.

‍♀️ if this helps

7 0

3 years ago

!!!!GIVING FIFTY POINTS T WHOEVER HELPS ME PLEASE!!!!

nadezda [96]

Answer:

14)9

15)6

16)57

17)29

4 0

3 years ago

Which is a correct first step for solving this equation? - 32 + 2 - 52 - 7 = 4x + 2